| Abstrakt: |
For an elliptic equation of the second order with variable discontinuous coefficients and the right side, a scheme of the fourth order of accuracy is constructed. On the jump line, the docking conditions (Kirchhoff) are assumed to be satisfied. The use of Richardson's extrapolation, as the numerical experiments show, increases the order of accuracy to about the sixth order. It is shown that relaxation methods, including multigrid methods, are applicable to solve such systems of linear algebraic equations (SLAEs) corresponding to a compact finite-difference approximation of the problem. In comparison with the classical approximation, the accuracy increases by a factor of about 100 with the same complexity. Various variants of the equation and boundary conditions are considered, as well as the problem of determining the eigenvalues and functions for a piecewise constant coefficient of the equation. [ABSTRACT FROM AUTHOR] |
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